$\dfrac{ 7v + w }{ 9 } = \dfrac{ -3v - 8x }{ 5 }$ Solve for $v$.
Multiply both sides by the left denominator. $\dfrac{ 7v + w }{ {9} } = \dfrac{ -3v - 8x }{ 5 }$ ${9} \cdot \dfrac{ 7v + w }{ {9} } = {9} \cdot \dfrac{ -3v - 8x }{ 5 }$ $7v + w = {9} \cdot \dfrac { -3v - 8x }{ 5 }$ Multiply both sides by the right denominator. $7v + w = 9 \cdot \dfrac{ -3v - 8x }{ {5} }$ ${5} \cdot \left( 7v + w \right) = {5} \cdot 9 \cdot \dfrac{ -3v - 8x }{ {5} }$ ${5} \cdot \left( 7v + w \right) = 9 \cdot \left( -3v - 8x \right)$ Distribute both sides ${5} \cdot \left( 7v + w \right) = {9} \cdot \left( -3v - 8x \right)$ ${35}v + {5}w = -{27}v - {72}x$ Combine $v$ terms on the left. ${35v} + 5w = -{27v} - 72x$ ${62v} + 5w = -72x$ Move the $w$ term to the right. $62v + {5w} = -72x$ $62v = -72x - {5w}$ Isolate $v$ by dividing both sides by its coefficient. ${62}v = -72x - 5w$ $v = \dfrac{ -72x - 5w }{ {62} }$